The individual components present in an electrical circuit are called circuit elements. The basic circuit elements describe physical processes such as the energy storage in a magnetic field (inductor), the energy storage in an electric field (capacitor) and the dissipation of electromagnetic energy (resistance). The behavior of these circuit elements may be completely described by their terminal voltage-current relationships within the time domain or the frequency domain.
Practical versions of these circuit elements deviate from the idealized model at high frequencies due to parasitic impedance effects. For a resistor, in general, there are reactive effects due to the winding of the resistance wire and the stray capacitance across the resistor. The practical version of an inductor is not a lossless element, and the effect of energy dissipation by resistive heating is observed. Practical capacitors are also lossy because of losses in the dielectric, and the terminal wires also have an inductive effect.
Circuit elements having predetermined values n-ay be selected and combined in a network to produce a prescribed output in response to a defined excitation to its input. The desired circuit behavior, such as frequency response, can be adversely affected by parasitic impedances. Moreover, some circuits may require the use of variable resistors, inductors and capacitors. Variable inductors and variable capacitors can be realized with the aid of mechanical devices, but at substantial increases in component size and mass, increases in dissipation and parasitic effects and increases in production costs with corresponding reductions in marketing revenues.
Generally, the inductance of a coil is proportional to the number of winding turns and the cross-sectional area of the coil structure. These values are not conveniently subject to continuous user variation, and the physical size and weight of an inductor will increase as higher inductance values are realized. An increase in the number of winding turns increases the resistance of the winding, which can vary from around one ohm per 1,000 feet for No. 12 gauge wire, to over 1,600 ohms per 1,000 feet for No. 42 gauge wire. The inductance value can also be increased by increasing the permeability of the core. However, losses in the heating of magnetic cores due to eddy currents and hysteresis increase in direct proportion to frequency. Dielectric losses in the coil winding insulation also increase at higher frequencies and are determined by the power factor of the distributive capacity. Moreover, most ferrite core materials will saturate in response to AC flux densities in the region of 3,000 to 4,000 Gauss. Thus the use of magnetic cores to vary the inductance value introduces losses which limit the performance of the inductor at high frequencies.
The selection of practical capacitors for use in a specific network is also limited by parasitic elements such as inductance and resistance. Moreover, since miniaturization is usually a prime consideration, the smallest possible capacitors will require thin dielectrics and efficient packaging without degrading performance. This severely limits prospects for user variation of the capacitance. Another important consideration in the selection of capacitors for use in certain LC filters is the figure of merit Q which is inversely proportional to the excitation frequency. The capacitor figure of merit Q must be sufficiently higher than the inductor figure of merit so that the effective figure of merit of the LC combination will not be degraded.
In certain LC filters, particularly those for radio frequency use, it is sometimes found more convenient to resonate a tuned circuit by adjusting the capacitance C rather than the inductance L. In such circuits, a small variable trimmer capacitor is connected in parallel with a fixed resonating capacitor. Such a parallel capacitance can be varied from its mean value by only a small percentage. The trimmer capacitors usually employ air, ceramic, mica or glass as a dielectric. Air capacitors consist of two sets of plates, one called a rotor, which is mounted on a shaft, and the other called the stator, which is fixed. As the rotor is revolved, the plates intermesh without making contact, resulting in increasing capacitance. For a large range capacitance variation, the plate size and number must be increased dramatically, especially if air is used as the dielectric. This becomes a serious limitation when the component mass or the available component space is restricted.
The resistor R is a fundamental component of active filters. Sensitivity studies have shown that the resistor components are usually at least as significant as capacitors. Accordingly, the selection of the appropriate resistor is critical to the success of a particular network design. In some networks, it is desirable to provide an identically constant negative resistance for exciting natural oscillation in passive LC circuits. However, the realization of such absolutely negative resistance values is not possible without the use of active elements.
It will be appreciated, therefore, that the parasitic effects associated with conventional inductors, capacitors and resistors, as well as constraints on physical size and mass, impose serious limitations on the design of networks which utilize passive R, L and C circuit elements, exclusively.